simulation.py
# This file was autogenerated from the template: simulation.py.template (2022-10-10 15:55:47).
import numpy as np
import system_model
from scipy.integrate import solve_ivp, odeint
from ackrep_core import ResultContainer
from ackrep_core.system_model_management import save_plot_in_dir
import matplotlib.pyplot as plt
import os
from ipydex import Container
# link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
def simulate():
"""
simulate the system model with scipy.integrate.solve_ivp
:return: result of solve_ivp, might contains input function
"""
model = system_model.Model()
rhs_xx_pp_symb = model.get_rhs_symbolic()
rhs = model.get_rhs_func()
# initial state values
xx0 = np.ones(model.sys_dim)
t_end = 10
tt = np.linspace(0, t_end, 1000)
simulation_data = solve_ivp(rhs, (0, t_end), xx0, t_eval=tt)
# using odeint for models with large state vectors
# res = odeint(rhs, y0=xx0, t=tt, tfirst=True)
# simulation_data = Container()
# simulation_data.y = res.transpose()
# simulation_data.t = tt
# postprocessing: calc output
ny = 2
C = model.get_parameter_value("C")
D21 = model.get_parameter_value("D21")
output = np.zeros((ny, len(tt)))
for i in range(len(tt)):
output[:,i] = np.matmul(C, simulation_data.y[:,i]) # + np.matmul(D21, w)
simulation_data.output = output
save_plot(simulation_data)
return simulation_data
def save_plot(simulation_data):
"""
plot your data and save the plot
access to data via: simulation_data.t array of time values
simulation_data.y array of data components
simulation_data.uu array of input values
:param simulation_data: simulation_data of system_model
:return: None
"""
for i in range(simulation_data.output.shape[0]):
plt.plot(simulation_data.t, simulation_data.output[i], label=f"$y_{i}$")
plt.legend()
plt.tight_layout()
save_plot_in_dir()
def evaluate_simulation(simulation_data):
"""
assert that the simulation results are as expected
:param simulation_data: simulation_data of system_model
:return:
"""
expected_final_state = np.zeros(240)
rc = ResultContainer(score=1.0)
simulated_final_state = simulation_data.y[:, -1]
rc.final_state_errors = [
simulated_final_state[i] - expected_final_state[i] for i in np.arange(0, len(simulated_final_state))
]
rc.success = np.allclose(expected_final_state, simulated_final_state, rtol=0, atol=1e-2)
return rc
system_model.py
# This file was autogenerated from the template: system_model.py.template (2022-10-10 15:55:47).
import sympy as sp
import numpy as np
import symbtools as st
import importlib
import sys, os
#from ipydex import IPS, activate_ips_on_exception
from ackrep_core.system_model_management import GenericModel, import_parameters
# Import parameter_file
params = import_parameters()
#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
class Model(GenericModel):
def initialize(self):
"""
this function is called by the constructor of GenericModel
:return: None
"""
# Define number of inputs -- MODEL DEPENDENT
self.u_dim = 1
# Set "sys_dim" to constant value, if system dimension is constant
self.sys_dim = 240
# check existence of params file
self.has_params = True
self.params = params
# ----------- SET DEFAULT INPUT FUNCTION ---------- #
def uu_default_func(self):
"""
define input function
:return:(function with 2 args - t, xx_nv) default input function
"""
def uu_rhs(t, xx_nv):
"""
sequence of numerical input values
:param t:(scalar or vector) time
:param xx_nv:(vector or array of vectors) numeric state vector
:return:(list) numeric inputs
"""
u = np.zeros(self.u_dim)
return u
return uu_rhs
# ----------- SYMBOLIC RHS FUNCTION ---------- #
def get_rhs_symbolic(self):
"""
define symbolic rhs function
:return: matrix of symbolic rhs-functions
"""
if self.dxx_dt_symb is not None:
return self.dxx_dt_symb
x = self.xx_symb
A, B, B1, C1, C, D11, D12, D21 = self.pp_symb # parameters
w = np.zeros(1) # noise
u = self.uu_symb # inputs
# define symbolic rhs functions
self.dxx_dt_symb = np.matmul(A,x) + np.matmul(B1,w) + np.matmul(B,u)
return self.dxx_dt_symb
parameters.py
# This file was autogenerated from the template: parameters.py.template (2022-10-10 15:55:47).
import sys
import os
import numpy as np
import sympy as sp
import tabulate as tab
#link to documentation with examples: https://ackrep-doc.readthedocs.io/en/latest/devdoc/contributing_data.html
# set model name
model_name = 'Perturbetd linear cable mass problem of order 20'
# ---------- create symbolic parameters
A = sp.MatrixSymbol('A', 240, 240)
B = sp.MatrixSymbol('B', 240, 1)
B1 = sp.MatrixSymbol('B1', 240, 1)
C1 = sp.MatrixSymbol('C1', 3, 240)
C = sp.MatrixSymbol('C', 2, 240)
D11 = sp.MatrixSymbol('D11', 3, 1)
D12 = sp.MatrixSymbol('D12', 3, 1)
D21 = sp.MatrixSymbol('D21', 2, 1)
pp_symb = [A, B, B1, C1, C, D11, D12, D21]
# ---------- create auxiliary symbolic parameters
# set numerical values of auxiliary parameters
# trailing "_nv" stands for "numerical value"
A_nv = sp.Matrix(np.array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
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3.14257562e-25, -1.17282519e-24, 4.37704319e-24,
-1.63353476e-23, 6.09643471e-23, -2.27522041e-22,
8.49123816e-22, -3.16897322e-21, 1.18267691e-20,
-4.41381031e-20, 1.64725643e-19, -6.14764470e-19,
2.29433224e-18, -8.56256447e-18, 3.19559257e-17,
-1.19261138e-16, 4.45088627e-16, -1.66109337e-15,
6.19928485e-15, -2.31360460e-14, 8.63448993e-14,
-3.22243551e-13, 1.20262931e-12, -4.48827367e-12,
1.67504654e-11, -6.25135878e-11, 2.33303886e-10,
-8.70701956e-10, 3.24950394e-09, -1.21273138e-08,
4.52597512e-08, -1.68911691e-07, 6.30387014e-07,
-2.35263636e-06, 8.78015844e-06, -3.27679974e-05,
1.22291831e-04, -4.56399327e-04, 1.70330548e-03,
-6.35682258e-03, 2.37239849e-02, -8.85391168e-02,
3.30432482e-01, -1.23319081e+00, 4.60233077e+00,
-1.71761323e+01, 6.41021983e+01, -5.05624552e+01,
9.63108896e-71, -3.85243558e-70, 1.44466334e-69,
-5.39340981e-69, 2.01289759e-68, -7.51224938e-68,
2.80360999e-67, -1.04632150e-66, 3.90492502e-66,
-1.45733786e-65, 5.43885892e-65, -2.02980978e-64,
7.57535324e-64, -2.82716032e-63, 1.05511060e-62,
-3.93772635e-62, 1.46957948e-61, -5.48454528e-61,
2.04686017e-60, -7.63898614e-60, 2.85090844e-59,
-1.06397351e-58, 3.97080321e-58, -1.48192393e-57,
5.53061541e-57, -2.06405377e-56, 7.70315354e-56,
-2.87485604e-55, 1.07291088e-54, -4.00415792e-54,
1.49437208e-53, -5.57707253e-53, 2.08139180e-52,
-7.76785996e-52, 2.89900480e-51, -1.08192332e-50,
4.03779281e-50, -1.50692479e-49, 5.62391988e-49,
-2.09887547e-48, 7.83310990e-48, -2.92335641e-47,
1.09101147e-46, -4.07171022e-46, 1.51958294e-45,
-5.67116075e-45, 2.11650601e-44, -7.89890795e-44,
2.94791258e-43, -1.10017595e-42, 4.10591255e-42,
-1.53234742e-41, 5.71879844e-41, -2.13428464e-40,
7.96525870e-40, -2.97267502e-39, 1.10941742e-38,
-4.14040217e-38, 1.54521913e-37, -5.76683629e-37,
2.15221261e-36, -8.03216679e-36, 2.99764546e-35,
-1.11873651e-34, 4.17518151e-34, -1.55819895e-33,
5.81527766e-33, -2.17029117e-32, 8.09963691e-32,
-3.02282565e-31, 1.12813389e-30, -4.21025300e-30,
1.57128781e-29, -5.86412594e-29, 2.18852159e-28,
-8.16767378e-28, 3.04821735e-27, -1.13761020e-26,
4.24561908e-26, -1.58448661e-25, 5.91338454e-25,
-2.20690515e-24, 8.23628216e-24, -3.07382235e-23,
1.14716612e-22, -4.28128224e-22, 1.59779628e-21,
-5.96305691e-21, 2.22544313e-20, -8.30546685e-20,
3.09964243e-19, -1.15680230e-18, 4.31724497e-18,
-1.61121776e-17, 6.01314653e-17, -2.24413684e-16,
8.37523269e-16, -3.12567939e-15, 1.16651943e-14,
-4.35350978e-14, 1.62475197e-13, -6.06365690e-13,
2.26298756e-12, -8.44558456e-12, 3.15193507e-11,
-1.17631818e-10, 4.39007922e-10, -1.63839987e-09,
6.11459156e-09, -2.28199664e-08, 8.51652739e-08,
-3.17841129e-07, 1.18619924e-06, -4.42695584e-06,
1.65216241e-05, -6.16595406e-05, 2.30116538e-04,
-8.58806613e-04, 3.20510991e-03, 4.53847095e-02]]))
B_nv = sp.Matrix(np.array([[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[-8.02590746e-69],
[ 3.21036299e-68],
[-1.20388612e-67],
[ 4.49450818e-67],
[-1.67741466e-66],
[ 6.26020782e-66],
[-2.33634166e-65],
[ 8.71934587e-65],
[-3.25410418e-64],
[ 1.21444821e-63],
[-4.53238244e-63],
[ 1.69150815e-62],
[-6.31279437e-62],
[ 2.35596693e-61],
[-8.79258829e-61],
[ 3.28143862e-60],
[-1.22464957e-59],
[ 4.57045440e-59],
[-1.70571680e-58],
[ 6.36582178e-58],
[-2.37575703e-57],
[ 8.86644595e-57],
[-3.30900268e-56],
[ 1.23493661e-55],
[-4.60884618e-55],
[ 1.72004481e-54],
[-6.41929462e-54],
[ 2.39571337e-53],
[-8.94092400e-53],
[ 3.33679827e-52],
[-1.24531007e-51],
[ 4.64756044e-51],
[-1.73449317e-50],
[ 6.47321663e-50],
[-2.41583734e-49],
[ 9.01602768e-49],
[-3.36482734e-48],
[ 1.25577066e-47],
[-4.68659990e-47],
[ 1.74906289e-46],
[-6.52759159e-46],
[ 2.43613034e-45],
[-9.09176222e-45],
[ 3.39309185e-44],
[-1.26631912e-43],
[ 4.72596729e-43],
[-1.76375500e-42],
[ 6.58242329e-42],
[-2.45659382e-41],
[ 9.16813293e-41],
[-3.42159379e-40],
[ 1.27695619e-39],
[-4.76566537e-39],
[ 1.77857053e-38],
[-6.63771558e-38],
[ 2.47722918e-37],
[-9.24514516e-37],
[ 3.45033515e-36],
[-1.28768261e-35],
[ 4.80569691e-35],
[-1.79351050e-34],
[ 6.69347233e-34],
[-2.49803788e-33],
[ 9.32280429e-33],
[-3.47931793e-32],
[ 1.29849913e-31],
[-4.84606472e-31],
[ 1.80857597e-30],
[-6.74969743e-30],
[ 2.51902137e-29],
[-9.40111575e-29],
[ 3.50854416e-28],
[-1.30940651e-27],
[ 4.88677161e-27],
[-1.82376799e-26],
[ 6.80639482e-26],
[-2.54018113e-25],
[ 9.48008503e-25],
[-3.53801590e-24],
[ 1.32040551e-23],
[-4.92782045e-23],
[ 1.83908763e-22],
[-6.86356847e-22],
[ 2.56151862e-21],
[-9.55971765e-21],
[ 3.56773520e-20],
[-1.33149690e-19],
[ 4.96921409e-19],
[-1.85453595e-18],
[ 6.92122237e-18],
[-2.58303536e-17],
[ 9.64001918e-17],
[-3.59770414e-16],
[ 1.34268146e-15],
[-5.01095544e-15],
[ 1.87011403e-14],
[-6.97936057e-14],
[ 2.60473283e-13],
[-9.72099525e-13],
[ 3.62792482e-12],
[-1.35395997e-11],
[ 5.05304742e-11],
[-1.88582297e-10],
[ 7.03798713e-10],
[-2.62661256e-09],
[ 9.80265151e-09],
[-3.65839935e-08],
[ 1.36533322e-07],
[-5.09549296e-07],
[ 1.90166386e-06],
[-7.09710616e-06],
[ 2.64867608e-05],
[-9.88499369e-05],
[ 3.68912987e-04],
[-1.37680201e-03],
[ 5.13829505e-03],
[-1.91763782e-02],
[ 7.15672178e-02],
[-2.67092493e-01],
[ 9.96802754e-01]]))
B1_nv = sp.Matrix(np.array([[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[-8.02590746e-69],
[ 3.21036299e-68],
[-1.20388612e-67],
[ 4.49450818e-67],
[-1.67741466e-66],
[ 6.26020782e-66],
[-2.33634166e-65],
[ 8.71934587e-65],
[-3.25410418e-64],
[ 1.21444821e-63],
[-4.53238244e-63],
[ 1.69150815e-62],
[-6.31279437e-62],
[ 2.35596693e-61],
[-8.79258829e-61],
[ 3.28143862e-60],
[-1.22464957e-59],
[ 4.57045440e-59],
[-1.70571680e-58],
[ 6.36582178e-58],
[-2.37575703e-57],
[ 8.86644595e-57],
[-3.30900268e-56],
[ 1.23493661e-55],
[-4.60884618e-55],
[ 1.72004481e-54],
[-6.41929462e-54],
[ 2.39571337e-53],
[-8.94092400e-53],
[ 3.33679827e-52],
[-1.24531007e-51],
[ 4.64756044e-51],
[-1.73449317e-50],
[ 6.47321663e-50],
[-2.41583734e-49],
[ 9.01602768e-49],
[-3.36482734e-48],
[ 1.25577066e-47],
[-4.68659990e-47],
[ 1.74906289e-46],
[-6.52759159e-46],
[ 2.43613034e-45],
[-9.09176222e-45],
[ 3.39309185e-44],
[-1.26631912e-43],
[ 4.72596729e-43],
[-1.76375500e-42],
[ 6.58242329e-42],
[-2.45659382e-41],
[ 9.16813293e-41],
[-3.42159379e-40],
[ 1.27695619e-39],
[-4.76566537e-39],
[ 1.77857053e-38],
[-6.63771558e-38],
[ 2.47722918e-37],
[-9.24514516e-37],
[ 3.45033515e-36],
[-1.28768261e-35],
[ 4.80569691e-35],
[-1.79351050e-34],
[ 6.69347233e-34],
[-2.49803788e-33],
[ 9.32280429e-33],
[-3.47931793e-32],
[ 1.29849913e-31],
[-4.84606472e-31],
[ 1.80857597e-30],
[-6.74969743e-30],
[ 2.51902137e-29],
[-9.40111575e-29],
[ 3.50854416e-28],
[-1.30940651e-27],
[ 4.88677161e-27],
[-1.82376799e-26],
[ 6.80639482e-26],
[-2.54018113e-25],
[ 9.48008503e-25],
[-3.53801590e-24],
[ 1.32040551e-23],
[-4.92782045e-23],
[ 1.83908763e-22],
[-6.86356847e-22],
[ 2.56151862e-21],
[-9.55971765e-21],
[ 3.56773520e-20],
[-1.33149690e-19],
[ 4.96921409e-19],
[-1.85453595e-18],
[ 6.92122237e-18],
[-2.58303536e-17],
[ 9.64001918e-17],
[-3.59770414e-16],
[ 1.34268146e-15],
[-5.01095544e-15],
[ 1.87011403e-14],
[-6.97936057e-14],
[ 2.60473283e-13],
[-9.72099525e-13],
[ 3.62792482e-12],
[-1.35395997e-11],
[ 5.05304742e-11],
[-1.88582297e-10],
[ 7.03798713e-10],
[-2.62661256e-09],
[ 9.80265151e-09],
[-3.65839935e-08],
[ 1.36533322e-07],
[-5.09549296e-07],
[ 1.90166386e-06],
[-7.09710616e-06],
[ 2.64867608e-05],
[-9.88499369e-05],
[ 3.68912987e-04],
[-1.37680201e-03],
[ 5.13829505e-03],
[-1.91763782e-02],
[ 7.15672178e-02],
[-2.67092493e-01],
[ 9.96802754e-01]]))
C1_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]))
C_nv = sp.Matrix(np.array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]]))
D11_nv = sp.Matrix(np.array([[0.],
[0.],
[0.]]))
D12_nv = sp.Matrix(np.array([[0. ],
[0. ],
[1.22474487]]))
D21_nv = sp.Matrix(np.array([[0.],
[1.]]))
# ---------- create symbolic parameter functions
# parameter values can be constant/fixed values OR set in relation to other parameters (for example: a = 2*b)
# list of symbolic parameter functions
# tailing "_sf" stands for "symbolic parameter function"
pp_sf = [A_nv, B_nv, B1_nv, C1_nv, C_nv, D11_nv, D12_nv, D21_nv]
# ---------- list for substitution
# -- entries are tuples like: (independent symbolic parameter, numerical value)
pp_subs_list = []
# OPTONAL: Dictionary which defines how certain variables shall be written
# in the table - key: Symbolic Variable, Value: LaTeX Representation/Code
# useful for example for complex variables: {Z: r"\underline{Z}"}
latex_names = {}
# ---------- Define LaTeX table
# Define table header
# DON'T CHANGE FOLLOWING ENTRIES: "Symbol", "Value"
tabular_header = ["Symbol", "Value"]
# Define column text alignments
col_alignment = ["center", "left"]
# Define Entries of all columns before the Symbol-Column
# --- Entries need to be latex code
col_1 = []
# contains all lists of the columns before the "Symbol" Column
# --- Empty list, if there are no columns before the "Symbol" Column
start_columns_list = []
# Define Entries of the columns after the Value-Column
# --- Entries need to be latex code
col_4 = []
# contains all lists of columns after the FIX ENTRIES
# --- Empty list, if there are no columns after the "Value" column
end_columns_list = []